Private weather station?

It's pretty much impossible to make reliable forecasts based on the data of a singular weather station. The initial data comes in from a variety of sources including satellites, radars, surface observation stations (weather stations) and upper air soundings around the globe. All of the above are maintained by public sector organizations who collaborate and share the data because the weather is an inescapably global thing. During WW2 the Germans actually set foot in Canada to set up a weather station in an attempt to spread the coverage of their observation network.

Nowadays all that data is used as inputs for numerical weather prediction models, running on supercomputers in the basements of meteorological institutes and agencies. Big global ones like ECMWF and GFS are used pretty much by all meteorologists around the world, who look at those and other smaller, more local models. They compare the different forecasts and critically evaluate the probabilities of different outcomes. They apply their own judgement selecting the most credible raw forecast and then edit that if needed. All in all, it's a very global effort.

At least where myself and @Kusimulkku@lemm.ee are from, meteorologists at the public broadcasting company (where that title is a requirement for getting the job) collaborate closely with their colleagues at the national meteorological institute. Their job is to comprehend the situation as presented by the institute, decide which bits of it are important, and then boil that down into a smooth and easy to understand presentation.

If a weather reporter isn't an actual meteorologist, then there is an actual meteorologist behind the scenes who made the presentation for the reporter to present.

Where I live I think they're all meteorologists or similar. That's why I'm wondering what's the situation in Mexico

I am willing to wager that in America, at least 95% of the people who report the weather live have degrees in meteorology or a related field. I almost took that career path.